Transmission line



Oct. 13, 1942. P. H. SMITH TRANSMISSION LINE Filed Aug. 19, 1959 3 m G G A H a wA m Wm ID 2 m M6 irllLllllll 4 3 2 INVENTOR P. H. 5114/ TH ATTORNEY conductor line transmitting a Patented Oct. 13, 1942 UNITED STATES PATENT OFFICE TRANSMISSION LINE Phillip H. Smith, Denville, N. L, assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application August 19, 1939, Serial No. 290,950 4 Claims. (01. 178-44) other gaseous medium, there is thus formed aline that possesses desirable characteristics for broad band signaling transmission, Such transmission line is disclosed in the patent of-L. Fspenschied et al., No. 1,835,031 granted December 8, 1931. It is one. characteristic of this line that at high frequencies the current tends to flow at. the outer surface of the inner conductor and at inner diameter-of the'outer conductor and the outer diameter of the inner conductor so that the voltage applied across the conductors wouldhave a minimum tendency to cause flashover therebetween. The observance of'this optimum diameter ratio also provides substantially maximum power carrying capability for the transmission line.

The invention will be readilyunderstood from" the following description when taken together with the accompanying drawing in which:

F 1 shows a cross-section of a concentric conductor;- and Figs. 2 and 3 are curves illustrating the operatlon of Fig. 1 under certain conditions.

Referring to 8. a hollow outer conductor llof suitable electricalconducting material is the inner surface of the outer conductor so that.

when a voltage is applied to the line to eflect such current flow the relation between the sizes of the two conductors is vitally important in so far as flash-over therebetween ,is concerned.

This invention involves the discovery that fora given size of outer conductor there is an optimum size of inner conductor for use therewith so that a voltage applied to such line. as it is transmitting a predetermined amount of power, will have minimum tendency to cause flash-over between the conductors.

It is an object of the invention to obtain sub stantially maximum economy in a concentric predetermined amount of power thereover.

It is another object of the invention to provide substantiall maximum power carrying capabilityfor, a concentric. .conductor transmission line having a given size of outer conductor. It is a further object of the invention to minimize the tendency for flash-over in a concentric conductor transmission line having a given size of outer conductor and over which a predetermined amount of Power is to be transmitted.

As the most economical type of a concentric conductor line for the on of a Predetermined amountof power is one in which the outside diameter of the outer conductor is as small as possible, it is the practice'to determine thesize of this-conductor as the initial consideration in the design of such transmission line. Thereafter, the size' of the inner conductor is determined.

In accordance with this invention the determination of the size of the inner conductor is mounted concentrically with respect to an inner cylindrical electrical conductor l I which may be either a hollow or solid structure so as to constitute a high frequency transmission system in which high frequency signaling currents flow in one direction along the inner surface of the outer conductor and in an opposite direction along the outer surface of the inner conductor as preferably disclosed in the patent to L. Espenschied et a1,, supra. It is to be understood that insu-- lators for spacing the conductors may be of the ype shown in the patent of L. Espenschied et al., supra; or of the type illustrated in my copending application. Serial No. 197,765 filed March 24,

1938, now Patent No. 2,216,893, issued Oct. 8. 1940; Or other suitable type.

The determination of the diameter of the outer conductor of such line is usually influenced by practical considerations among which is that of economics. This aspect is of prime impo particularly in the design" oi concentric conductor lines in which the outer conductor has an outside diameter of the order ofv six inches, as the cost of copper is an important factor. The most economical design for a concentric conductor transmission line required to transmit a predetermined amount of power is ordinarily one that embodies an outer conductor having the smallest possible outside'diameter, as the major portion of the cost of such line is involved in the such as to observe an optimum ratio between the outer conductor. 1

Supplementing the above is the outstanding factor of voltage gradient at the surface of the inner conductor which gradient tends to cause flash-over between the inner and outer conductors when a critical value thereof is attained. Such flash-over is undesirable as it interrupts transmission and may deleteriously affect both conductors and insulators.

According to this invention it has been found that, assuming the selection of an outer conductor having a certain inner diameter, there is an optimum ratio of 1.648 to 1 between the inner diameter of the outer conductor and the outer diameter of the inner conductor which optimum ratio effects a minimum voltage gradientat the outer surface of the inner conductor for a predetermined power input to the concentric conductor line. This means that the voltage applied across the conductors under such conditions will have minimum tendency to cause flash-over therebetween. It is to be understood that such concentric conductor transmission line is terminated in its characteristic impedance.

Minimum voltage gradient for predetermined applied voltage, diameter ratio=e=2.718 to 1 From the standpoint of minimum tendency to flash-over between the inner and outer conductors of a concentric conductor transmission line for a predetermined input voltage thereto andv in which the inner diameter of the outer conductor possesses a predetermined value, the optimum conductor diameter ratio between outer and inner conductors is e=2.718 to 1, which corresponds to a characteristic impedance of 60.0

ohms. This is determined by minimizing the formula for the voltage gradient at the surface of the inner conductor where flash-over first occurs. ent at the surface of the inner conductor:

d log,

volts/cm. (1)

' to Fig. 2 which shows for a constant applied voltage the minimum voltage gradient on the outer surface of the inner conductor occurs for a conductor diameter ratio e 2.718 to 1; that the voltage gradient increases sharply for ratios less than 2.718 and increases gradually for ratios greater than 2.718. 1

.Minimum voltage gradient for a predetermined power transmitted, to 1 Consequently, from the standpoint of maximum power capability of a concentric conductor transmission line the optimum ratio between the inner diameter of the outer conductor and th e outer diameter of the inner conductor is =1.648 to- 1, which ratio corresponds to a characteristic impedance of 30.0 ohms. This is due to the fact that as the conductor diameter ratio is being reduced the characteristic impedance is also being reduced which impedance reduction in turn serves to reduce the voltage impressed on the line for a predetermined power applied thereto. Therefore, even though the gradient for apredetermined voltage is increasing the applied voltage is at first decreasing more rapidly than suchincreases. Eventually,

diameter ratio=' /E=1.s4s

as the conductor diameter ratio is being' reduced,

E=- /P Z volts (2) in which P is power in watts, but

substituting this value for Z0 into (2) E=J6 0T' 4103,? volts 4 I The gradient (9') at the surface of the inner conductor for a predetermined applied voltage is given by Equation 1. Substituting the above equivalent for E, Equation 4, in Equation 1, the following expression for the gradient at the surface of the inner conductor for a predetermined power is obtained:

The following equation gives the gradihowever, the rate at which the gradient increases,

volts/cm.

Let

2 /'6T)T=K and for minimum gradient 1 2 log, z 1

Nah-

Thus, when the diameter ratio of a concentric conductor line shown in Fig. 1 approximates that indicated in Equation 8 there will be substansurface of the inner conductor as a predetermined power is being transmitted over the line. This means that the line is provided with maximum power car y ng capability as the voltage applied to the line would have a minimum tendency to cause ilash-over-between the conductors thereof. Such tendency represents the usual power carrying limitation of a high frequency concentric ton line having air or inert gas as a dielectric at atmospheric pressure;

It is to be understood that while the invention is disclosed with reference to high frequency signaling systems, it is not necessarily limited thereto as it is also applicable with equal facility to power tron systems of either direct or conductors arranged concentrically so that one v serves as a return path for the other, the ratio of the inner diameter of the outer conductor to outer diameter of the inner conductor being of the order of 1.65 to 1 to obtain maximum economy of conductor material in said line for transmitting a predetermined amount of power there- 2. A concentric conductor tially minimum voltage gradient on the outer" the order of 1.65 to 1 to determine-substantially maximum power carrying capability ofthe line.

3. 'A concentric conductor transmission line comprising outer and inner cylindrical electrical conductors arranged concentrically so thatcne serves as a return path for the other and'insu- ,lated from each other by a dielectric that is largely gaseous, the ratio of the inner diameter eter of the inner conductor being such value that the characteristic impedance of the line is approximately 30 ohms.

4. A concentric conductor transmission line comprising outer and inner cylindrical electrical conductors arranged concentrically so that one serves as a return path for the other", the ratio of the inner diameter of a given outer, conductor to the outer diameter of the inner conductor being approximately 1.65 to 1 so that the voltage applied to the. line will have substantially minimum tendency to cause flash-over between the conductors as a predetermined amount ofpower is being transmitted over the line.

rnnmpn. sun-m. 

